Stratification of Hermitian Matrices and the Alexander Mapping
نویسنده
چکیده
The space of Hermitian matrices is stratiied according to the multiplicities of the eigenvalues. This stratiication is responsible for the quantum Hall eeect. We study the simplest properties of this stratiication: give explicit expressions for the Poincar e duality and the Alexander mapping, and prove that the spectral sequence generated by the ltration by matrices having at most i diierent eigenvalues degenerates in term E 2. Stratiication des matrices hermitiennes et l'application d'Alexander R esum e. L'espace des matrices hermitiennes est stratii e par les multiplicit es des valeurs propres. Cette stratiication engendre l'eeet de Hall quantique. Nous etudions des pro-priet es tres simple de cette stratiication: nous donnons des expressions explicites pour la dualit e de Poincar e et l'application d'Alexander, et nous demonstrons que la suite spectrale engendr ee per la ltration per des matrices ayant tout en plus i valeurs propres diierents d eg en ere en un terme E 2 .
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